Jump-starting coordination in a stag hunt: Motivation, mechanisms, and their analysis

The stag hunt (or assurance game) is a simple game that has been used as a prototype of a variety of social coordination problems (ranging from the social contract to the adoption of technical standards). Players have the option to either use a superior cooperative strategy whose payoff depends on the other players' choices or use an inferior strategy whose payoff is independent of what other players do; the cooperative strategy may incur a loss if sufficiently many other players do not cooperate. Stag hunts have two (strict) pure Nash equilibria, namely, universal cooperation and universal defection (as well as a mixed equilibrium of low predictive value). Selection of the inferior (pure) equilibrium is called a coordination failure. In this paper, we present and analyze using game-theoretic techniques mechanisms aiming to avert coordination failures and incite instead selection of the superior equilibrium. Our analysis is based on the solution concepts of Nash equilibrium, dominance solvability, as well as a formalization of the notion of "incremental deployability," which is shown to be keenly relevant to the sink equilibrium.Comment: Some overlap with arXiv:1210.778

Power Allocation Games in Interference Relay Channels: Existence Analysis of Nash Equilibria

We consider a network composed of two interfering point-to-point links where the two transmitters can exploit one common relay node to improve their individual transmission rate. Communications are assumed to be multi-band and transmitters are assumed to selfishly allocate their resources to optimize their individual transmission rate. The main objective of this paper is to show that this conflicting situation (modeled by a non-cooperative game) has some stable outcomes, namely Nash equilibria. This result is proved for three different types of relaying protocols: decode-and-forward, estimate-and-forward, and amplify-and-forward. We provide additional results on the problems of uniqueness, efficiency of the equilibrium, and convergence of a best-response based dynamics to the equilibrium. These issues are analyzed in a special case of the amplify-and-forward protocol and illustrated by simulations in general.Comment: To appear in EURASIP Journal on Wireless Communications and Networking (JWCN

Agame-theoretical approach to network capacity planning under competition

The paper discusses the dimensioning strategies of two network providers (operators) that supply channels to the same population of users in a competitive environment. Usersare assumed to compete for best service (lowest blocking probability of new request), while operators wishto maximize their profits. This setting gives rise to two interconnected, noncooperative games: a) a users game, in which the partition of primary traffic between operators is determined by the operators' channel capacities and by the users' blocking-avoidance strategy; and b) a network dimensioning game between operators in which the players alternate dimensioning decisions thatmaximize their profit rate under the current channel capacity of his/her opponent. At least for two plausible users' blocking avoidance strategies discussed in the paper, the users game will always reach some algorithmic equilibrium. In the operators' game, the player strategies are given by their numbers of deployed chanels, limited by their available infrastructure resources. If the infrastrucutre is under-dimensioned with respect to the traffic rate, the operators game willreach a Nash equilibrium when both players reach full use of their available infrastructures. Otherweise, a Nash equilibrium may also arise if both operators incur the same deployment costs. If costs are asymmetric, though, the alternating game may enter a loop. If the asymmetry is modest, both players may then try to achieve a competitive monopoly in which the opponent is forced to leave the game or operate with a loss (negative profit). However, if the asymmetry is high enough, only the player with the lower costs can force his opponent to leave the game while still holding a profitable operation. --network dimensioning,game theory,duopoly,Nash equilibrium,circuit switching,blocking probability

Prices of Anarchy, Information, and Cooperation in Differential Games

The price of anarchy (PoA) has been widely used in static games to quantify the loss of efficiency due to noncooperation. Here, we extend this concept to a general differential games framework. In addition, we introduce the price of information (PoI) to characterize comparative game performances under different information structures, as well as the price of cooperation to capture the extent of benefit or loss a player accrues as a result of altruistic behavior. We further characterize PoA and PoI for a class of scalar linear quadratic differential games under open-loop and closed-loop feedback information structures. We also obtain some explicit bounds on these indices in a large population regime

Approximate Best-Response Dynamics in Random Interference Games

In this paper we develop a novel approach to the convergence of Best-Response Dynamics for the family of interference games. Interference games represent the fundamental resource allocation conflict between users of the radio spectrum. In contrast to congestion games, interference games are generally not potential games. Therefore, proving the convergence of the best-response dynamics to a Nash equilibrium in these games requires new techniques. We suggest a model for random interference games, based on the long term fading governed by the players' geometry. Our goal is to prove convergence of the approximate best-response dynamics with high probability with respect to the randomized game. We embrace the asynchronous model in which the acting player is chosen at each stage at random. In our approximate best-response dynamics, the action of a deviating player is chosen at random among all the approximately best ones. We show that with high probability, with respect to the players' geometry and asymptotically with the number of players, each action increases the expected social-welfare (sum of achievable rates). Hence, the induced sum-rate process is a submartingale. Based on the Martingale Convergence Theorem, we prove convergence of the strategy profile to an approximate Nash equilibrium with good performance for asymptotically almost all interference games. We use the Markovity of the induced sum-rate process to provide probabilistic bounds on the convergence time. Finally, we demonstrate our results in simulated examples

A Passivity-Based Approach to Nash Equilibrium Seeking over Networks

In this paper we consider the problem of distributed Nash equilibrium (NE) seeking over networks, a setting in which players have limited local information. We start from a continuous-time gradient-play dynamics that converges to an NE under strict monotonicity of the pseudo-gradient and assumes perfect information, i.e., instantaneous all-to-all player communication. We consider how to modify this gradient-play dynamics in the case of partial, or networked information between players. We propose an augmented gradient-play dynamics with correction in which players communicate locally only with their neighbours to compute an estimate of the other players' actions. We derive the new dynamics based on the reformulation as a multi-agent coordination problem over an undirected graph. We exploit incremental passivity properties and show that a synchronizing, distributed Laplacian feedback can be designed using relative estimates of the neighbours. Under a strict monotonicity property of the pseudo-gradient, we show that the augmented gradient-play dynamics converges to consensus on the NE of the game. We further discuss two cases that highlight the tradeoff between properties of the game and the communication graph.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Nash and Wardrop equilibria in aggregative games with coupling constraints

We consider the framework of aggregative games, in which the cost function of each agent depends on his own strategy and on the average population strategy. As first contribution, we investigate the relations between the concepts of Nash and Wardrop equilibrium. By exploiting a characterization of the two equilibria as solutions of variational inequalities, we bound their distance with a decreasing function of the population size. As second contribution, we propose two decentralized algorithms that converge to such equilibria and are capable of coping with constraints coupling the strategies of different agents. Finally, we study the applications of charging of electric vehicles and of route choice on a road network.Comment: IEEE Trans. on Automatic Control (Accepted without changes). The first three authors contributed equall

A Unified Mechanism Design Framework for Networked Systems

Mechanisms such as auctions and pricing schemes are utilized to design strategic (noncooperative) games for networked systems. Although the participating players are selfish, these mechanisms ensure that the game outcome is optimal with respect to a global criterion (e.g. maximizing a social welfare function), preference-compatible, and strategy-proof, i.e. players have no reason to deceive the designer. The mechanism designer achieves these objectives by introducing specific rules and incentives to the players; in this case by adding resource prices to their utilities. In auction-based mechanisms, the mechanism designer explicitly allocates the resources based on bids of the participants in addition to setting prices. Alternatively, pricing mechanisms enforce global objectives only by charging the players for the resources they have utilized. In either setting, the player preferences represented by utility functions may be coupled or decoupled, i.e. they depend on other player's actions or only on player's own actions, respectively. The unified framework and its information structures are illustrated through multiple example resource allocation problems from wireless and wired networks

Potential Games for Energy-Efficient Resource Allocation in Multipoint-to-Multipoint CDMA Wireless Data Networks

The problem of noncooperative resource allocation in a multipoint-to-multipoint cellular network is considered in this paper. The considered scenario is general enough to represent several key instances of modern wireless networks such as a multicellular network, a peer-to-peer network (interference channel), and a wireless network equipped with femtocells. In particular, the problem of joint transmit waveforms adaptation, linear receiver design, and transmit power control is examined. Several utility functions to be maximized are considered, and, among them, we cite the received SINR, and the transmitter energy efficiency, which is measured in bit/Joule, and represents the number of successfully delivered bits for each energy unit used for transmission. Resorting to the theory of potential games, noncooperative games admitting Nash equilibria in multipoint-to-multipoint cellular networks regardless of the channel coefficient realizations are designed. Computer simulations confirm that the considered games are convergent, and show the huge benefits that resource allocation schemes can bring to the performance of wireless data networks.Comment: Submitted to Physical Communication, ELSEVIE

Network Formation Games Among Relay Stations in Next Generation Wireless Networks

The introduction of relay station (RS) nodes is a key feature in next generation wireless networks such as 3GPP's long term evolution advanced (LTE-Advanced), or the forthcoming IEEE 802.16j WiMAX standard. This paper presents, using game theory, a novel approach for the formation of the tree architecture that connects the RSs and their serving base station in the \emph{uplink} of the next generation wireless multi-hop systems. Unlike existing literature which mainly focused on performance analysis, we propose a distributed algorithm for studying the \emph{structure} and \emph{dynamics} of the network. We formulate a network formation game among the RSs whereby each RS aims to maximize a cross-layer utility function that takes into account the benefit from cooperative transmission, in terms of reduced bit error rate, and the costs in terms of the delay due to multi-hop transmission. For forming the tree structure, a distributed myopic algorithm is devised. Using the proposed algorithm, each RS can individually select the path that connects it to the BS through other RSs while optimizing its utility. We show the convergence of the algorithm into a Nash tree network, and we study how the RSs can adapt the network's topology to environmental changes such as mobility or the deployment of new mobile stations. Simulation results show that the proposed algorithm presents significant gains in terms of average utility per mobile station which is at least 17.1% better relatively to the case with no RSs and reaches up to 40.3% improvement compared to a nearest neighbor algorithm (for a network with 10 RSs). The results also show that the average number of hops does not exceed 3 even for a network with up to 25 RSs.Comment: IEEE Transactions on Communications, vol. 59, no. 9, pp. 2528-2542, September 201